Five cylindrical resistors made of carbon with resistivity Ï=3.5x10–3 Ω.metr
ID: 2109921 • Letter: F
Question
Five cylindrical resistors made of carbon with resistivity Ï=3.5x10–3 Ω.metres are connected in a circuit as shown below. R1 has length 4 mm and diameter 1 mm. Each R2 is twice as long as R1. Each R3 has twice the diameter of R1.
A) Calculate the effective resistance between points A and B in the figure below.
B) If the current entering A is 0.25 mA, what is the potential difference across R2?
C) Which branch (R1-R2, R2 or R2-R3) has the greatest current through it?
Explanation / Answer
R1 = p*l/A = 17.83 ohm R2 = 2p*l/A = 35.66 ohm R3 = p*l/2A = 8.915 ohm a). 1/R(total) = 1/(R1+R2) +1/(R2+R3) +1/R2 => R(total)= 14.457 ohm b). V = I*R = 0.25*10^-3*14.457 = 3.6 *10^-3 V c). since R2 has least resistance, maximum current will pass through this branch
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